Messages are conveyed by arranging four white, one blue, and three red flags on a pole. Flags of the same color are alike. If a message is transmitted by the order in which the colors are arranged, the total number of messages that can be transmitted if exactly six flags are used is a. `45` b. `65` c. `125` d. `185`

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that atleast one ball is separated from the balls of the same color.

There are (n+1) white and (n+1) black balls, each set numbered 1ton+1. The number of ways in which the balls can be arranged in a row so that the adjacent balls are of different colors is a. (2n+2)! b. (2n+2)!xx2 c. (n+1)!xx2 d. 2{(n+1)!}^2

The total number of flags with three horizontal strips in order, which can be formed using 2 identical red, 2 identical green, and 2 identical white strips is equal to a. 4! b. 3xx(4!) c. 2xx(4!) d. none of these

A bag initially contains 1 red and 2 blue balls. An experiment consisting of selecting a ball at random, noting its color and replacing it together with an additional ball of the same color. If three such trials are made, then (A) Probability that a t least one blue ball is drawn is 0.9 (B) Probability that exactly one blue ball is drawn is 0.2 (C) Probability that all the drawn balls are red given that all the drawn balls are of same color is 0.2 (D) Probability that at least one red bal is drawn is 0.6

A library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^2(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !) (c !)^3)